Pullups are the best upper body bang for your buck exercise you can do. And there are limitless variations you can perform by adjusting grip type, Pronated, Supinated, Neutral. Or grip width from wide, medium and narrow. And then you can add weight via weight vests and plates.
In this short video I am doing dymanic chest to bar pullups. These are NOT meant to be done for high reps. I have to strap my legs into my chair so that pulls me back down a bit as I reach the top but the idea is to pull yourself up as high as you can. You want to bang your chest on the bar, whereas normal pullups you might do for reps you get your chin up to the bar and go back down. These should feel like an explosion where you are trying to pop your head up through the ceiling. I do sets of 2-3 reps at most, rest for 30 seconds, then go again.
My advice it to just start with singles. The pulling motion is so violent your legs will come off your footplate and even if your chair is locked, its likely to move around. I even have weight plates blocking the front tires, with my brakes on, and the chair still moves all over the place.
This will help increase your power output and acceleration. Which will help add more weight for weighted pull ups.